A new approach to compressed sensing (2012-2016)
Abstract
A digital camera taking a photograph, a mobile phone transmitting a voice, an MRI machine scanning a brain: these are all examples of signal sampling. In 2004 a revolutionary new approach to signal sampling and reconstruction, called compressed sensing, was introduced by several mathematicians including Fields Medallist Terry Tao. The investigators on this proposal recently discovered a novel approach to compressed sensing that involves the use of combinatorial objects known as hash families. This project will explore this new approach, develop a number of new mathematical tools for use in compressed sensing, produce more efficient compressed sensing algorithms, and demonstrate the effectiveness of hash families in this context.